Exam 10: Dynamics of Rotational Motion

A uniform disk,a uniform hoop,and a uniform solid sphere are released at the same time at the top of an inclined ramp.They all roll without slipping.In what order do they reach the bottom of the ramp?

In the figure,a mass of 31.77 kg is attached to a light string that is wrapped around a cylindrical spool of radius 10.0 cm and moment of inertia 4.00 kg • m².The spool is suspended from the ceiling,and the mass is then released from rest a distance 5.70 m above the floor.How long does it take to reach the floor?

A turntable has a radius of 0.80 m and a moment of inertia of 2.0 kg • m².The turntable is rotating with an angular velocity of 1.5 rad/s about a vertical axis though its center on frictionless bearings.A very small 0.40-kg ball is projected horizontally toward the turntable axis with a velocity of 3.0 m/s.The ball is caught by a very small and very light cup-shaped mechanism on the rim of the turntable (see figure).The percent of the initial kinetic energy of the system that is lost during the capture of the ball is closest to

A very thin horizontal,2.00-m long,5.00-kg uniform beam that lies along the east-west direction is acted on by two forces.At the east end of the beam,a 200-N force pushes downward.At the west end of the beam,a 200-N force pushes upward.What is the angular acceleration of the beam?

A uniform solid sphere of mass 1.5 kg and diameter 30.0 cm starts from rest and rolls without slipping down a 35° incline that is 7.0 m long. (a)Calculate the linear speed of the center of the sphere when it reaches the bottom of the incline. (b)Determine the angular speed of the sphere about its center at the bottom of the incline. (c)Through what angle (in radians)does this sphere turn as it rolls down the incline? (d)Does the linear speed in (a)depend on the radius or mass of the sphere? Does the angular speed in (b)depend on the radius or mass of the sphere?

A uniform solid disk of radius 1.60 m and mass 2.30 kg rolls without slipping to the bottom of an inclined plane.If the angular velocity of the disk is at the bottom,what is the height of the inclined plane?

An object is rotating with an angular momentum 4.00 kg • m²/s while being acted on by a constant torque .What is the angular speed of precession of the angular velocity of the object?

A tire is rolling along a road,without slipping,with a velocity v.A piece of tape is attached to the tire.When the tape is opposite the road (at the top of the tire),its velocity with respect to the road is

A metal bar is hanging from a hook in the ceiling when it is suddenly struck by a ball that is moving horizontally (see figure).The ball is covered with glue,so it sticks to the bar.During this collision

A bicycle is traveling north at 5.0 m/s.The mass of the wheel,2.0 kg,is uniformly distributed along the rim,which has a radius of 20 cm.What are the magnitude and direction of the angular momentum of the wheel about its axle?

The two rotating systems shown in the figure differ only in that the two identical movable masses are positioned at different distances from the axis of rotation.If you release the hanging blocks simultaneously from rest,and if the ropes do not slip,which block lands first?

A force = 3.00 N - 2.00 N acts at a location = 1.00 m + 2.00 m on an object.What is the torque that this force applies about an axis through the origin perpendicular to the xy-plane?

If an irregularly shaped object (such as a wrench)is dropped from rest in a classroom and feels no air resistance,it will

A solid,uniform sphere of mass 2.0 kg and radius 1.7 m rolls from rest without slipping down an inclined plane of height 7.0 m.What is the angular velocity of the sphere at the bottom of the inclined plane?

A uniform solid cylinder of radius R and a thin uniform spherical shell of radius R both roll without slipping.If both objects have the same mass and the same kinetic energy,what is the ratio of the linear speed of the cylinder to the linear speed of the spherical shell?

A 72.0-kg person pushes on a small doorknob with a force of 5.00 N perpendicular to the surface of the door.The doorknob is located 0.800 m from axis of the frictionless hinges of the door.The door begins to rotate with an angular acceleration of 2.00 rad/s².What is the moment of inertia of the door about the hinges?

A 500-g particle is located at the point = 4m + 3m - 2m and is moving with a velocity .What is the angular momentum of this particle about the origin?

Three solid,uniform,cylindrical flywheels,each of mass 65.0 kg and radius 1.47 m rotate independently around a common axis.Two of the flywheels rotate in one direction at the other rotates in the opposite direction at 3.42 rad/s.Calculate the magnitude of the net angular momentum of the system.

A string is wrapped around a pulley with a radius of 2.0 cm and no appreciable friction in its axle.The pulley is initially not turning.A constant force of 50 N is applied to the string,which does not slip,causing the pulley to rotate and the string to unwind.If the string unwinds 1.2 m in ,what is the moment of inertia of the pulley?

A light triangular plate OAB is in a horizontal plane.Three forces, and act on the plate,which is pivoted about a vertical axes through point O.In the figure, ₂ is perpendicular to OB.Consider the counterclockwise sense as positive.The sum of the torques about the vertical axis through point O,acting on the plate due to forces F₁,F₂,and F₃,is closest to